Acoustics of Layered Media I: Plane and Quasi-Plane Waves by Professor Leonid M. Brekhovskikh, Dr. Oleg A. Godin (auth.)

By Professor Leonid M. Brekhovskikh, Dr. Oleg A. Godin (auth.)

This monograph is dedicated to the systematic presentation of the idea of sound­ wave propagation in layered buildings. those buildings may be man-made, equivalent to ultrasonic filters, lenses, surface-wave hold up strains, or average media, equivalent to the sea and the ambience, with their marked horizontal stratification. A similar challenge is the propagation of elastic (seismic) waves within the earth's crust those issues were taken care of quite thoroughly within the publication via L. M. Brek­ hovskikh, Waves in Layered Media, the English model of the second one version of which was once released through educational Press in 1980. as a result of growth in experimental and computing device expertise it has develop into attainable to research the effect of things resembling medium movement and density stratification upon the propagation of sound waves. a lot cognizance has been paid to propagation thought in near-stratified media, Le. , media with small deviations from strict stratification. attention-grabbing effects have additionally been acquired within the fields of acoustics which were formerly thought of to be "completely" constructed. For those purposes, and likewise as a result of the influx of researchers from the comparable fields of physics and arithmetic, the circle of individuals and examine teams engaged within the examine of sound propagation has quite increased. consequently, the looks of a brand new precis overview of the sector of acoustics of layered media has turn into hugely fascinating. seeing that Waves in Layered Media grew to become fairly well known, we've got attempted to keep its confident positive factors and normal structure.

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Additional info for Acoustics of Layered Media I: Plane and Quasi-Plane Waves

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4) the refraction angle in the upper medium will be 8. 16) it will be -V for the wave incident from below at the angle 81. In particular, if 8 is the angle of complete transmission for the wave incident from above [V(8) = 0], then 81 is that angle for the wave incident from below. Such a simple role does not hold for the transmission coefficient W, however. 18), is invariant when one reverses the propagation direction of the wave (8, fl, and C are the refraction angle, density, and sound velocity of the medium where the refracted wave propagates).

V does not change if the signs of sin 61 and (112 - VI) are changed simultaneously. We assume, therefore, that sin 61 ~ O. In the reference system moving together with upper medium this means that the wave's system propagates in the direction of positive :E. The reftection coefficient V can be obtained for any incidence angle (under the assumption 61 ~ 0) by proper choosing the sign of the ftow velocity difference ± 1112 - vII· When the media are at rest there exist two possible types of reftection: IV I < 1 (partial reftection) and IVI = 1 (total reftection).

24). 3) Z - const op/o( This quantity has all the properties of the impedance discussed in previous sections for media at rest. It does not depend on horizontal coordinates, time, or the amplitude of the wave. Furthermore it is continuous across the interfaces between layers. 7). 24) we obtain . 4a) = -IWeo op/o( , or in ordinary coordinates Z = . -IWe ß2 P oploz . 3) is valid for waves of any physical nature provided that the corresponding wave equation is written as a one dimensional Helmholtz equation which does not contain the derivatives of the media parameters in the coefficients.

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